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Quadratic Lyapunov Functions for Mechanical Systems.

Center for Systems Science, Yale University, Report Number 8703, March 1987

D. E. Koditschek
Yale University
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Abstract
      The “mechanical systems” define a large and important class of highly nonlinear dynamical equations which, for example, encompasses all robots. In this report it is shown that a strict Lyapunov Function suggested by the simplest examplar of the class - a one degree of freedom linear time invariant dynamical system - may be generalized over the entire class. The report lists a number of standard but useful consequences of this discovery. The analysis suggests that the input-output properties of the entire class of nonlinear systems share many characteristics in common with those of a second order, phase canonical, linear time invariant differential equation.
BibTeX entry
@inproceedings{kod-yale-1987-1,
   title      = {Quadratic Lyapunov Functions for Mechanical Systems.},
   author     = {D.E. Koditschek},
   booktitle  = {Center for Systems Science, Yale University},
   year       = {1987},
   month      = {March},
}

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